您的位置:山东大学 -> 科技期刊社 -> 《山东大学学报(理学版)》

《山东大学学报(理学版)》 ›› 2023, Vol. 58 ›› Issue (3): 48-54.doi: 10.6040/j.issn.1671-9352.0.2022.461

• • 上一篇    下一篇

基于L-值泛代数的L-值模

周鑫1,2,刘淼1,2   

  1. 1. 伊犁师范大学数学与统计学院, 新疆 伊宁 835000;2. 伊犁师范大学应用数学研究所, 新疆 伊宁 835000
  • 发布日期:2023-03-02
  • 作者简介:周鑫(1981— ),男,博士,副教授,硕士生导师,研究方向为代数与序结构以及李代数. E-mail:zhoux566@nenu.edu.cn
  • 基金资助:
    新疆维吾尔自治区自然科学基金资助项目(2020D01C269);新疆维吾尔自治区高校科研计划项目(XJEDU2021Y042);新疆伊犁州科技计划项目(YZ2022Y010);伊犁师范大学博士科研启动基金项目(2021YSBS011);伊犁师范大学科研创新团队项目(CXZK2021014);伊犁师范大学学实高层次人才岗位项目(YSXSGG22002)

L-valued modules based on L-valued universal algebras

ZHOU Xin1,2, LIU Miao1,2   

  1. 1. College of Mathematics and Statistics, Yili Normal University, Yining 835000, Xinjiang, China;
    2. Institute of Applied Mathematics, Yili Normal University, Yining 835000, Xinjiang, China
  • Published:2023-03-02

摘要: L-值模是一类格值代数结构,定义在类似于模的泛代数上首先,将经典数学中等式用模糊恒等式替代,基于L-值泛代数给出了L-值模的概念其次, 通过模糊代数的商结构给出了L-值泛代数是L-值模的充分必要条件再者,给出了L-值模的基本性质最后, 给出了L-值子模的刻画

关键词: 模糊集, L-值集, L-值泛代数, L-值模, 模糊恒等式

Abstract: L-valued modules are lattice-valued algebraic structures, defined on universal algebras of the same type as modules, but which are not necessary modules. First, the classical equality is replaced by a fuzzy identity, and the concept of L-valued modules are given based on L-valued universal algebras. Next, the necessary and sufficient conditions for L-valued universal algebras to be L-valued modules are given by using quotient structure of fuzzy algebras. Furthermore, this gives some basic properties of L-valued modules. Finally, we shows the structure of L-valued submodules.

Key words: fuzzy set, L-valued set, L-valued universal algebra, L-valued module, fuzzy identity

中图分类号: 

  • O159
[1] ZADEH L A. Fuzzy sets[J]. Information and Control, 1965, 8(3):338-353.
[2] GOGUEN J A. L-fuzzy sets[J]. Journal of Mathematical Analysis and Applications, 1967, 18(1):145-174.
[3] ROSENFELD A. Fuzzy groups[J]. Journal of Mathematical Analysis and Applications, 1971, 35(3):512-517.
[4] DIXIT V N, KUMAR R, AJMAL N. On fuzzy rings[J]. Fuzzy Sets and Systems, 1992, 49(2):205-213.
[5] NANDA S. Fuzzy fields and fuzzy linear spaces[J]. Fuzzy Sets and Systems, 1986, 19(1):89-94.
[6] MALIK D S, MORDESON J N. Fuzzy vector spaces[J]. Information Sciences, 1991, 55(1/2/3):271-281.
[7] PAN F Z. Fuzzy finitely generated modules[J]. Fuzzy Sets and Systems, 1987, 21(1):105-113.
[8] LÓPEZ-PERMOUTH S R, MALIK D S. On categories of fuzzy modules[J]. Information Sciences, 1990, 52(2):211-220.
[9] YEHIA S E B. Fuzzy ideals and fuzzy subalgebras of Lie algebras[J]. Fuzzy Sets and Systems, 1996, 80(2):237-244.
[10] KIM C G, LEE D S. Fuzzy lie ideals and fuzzy Lie subalgebras[J]. Fuzzy Sets and Systems, 1998, 94(1):101-107.
[11] FOURMAN M P, SCOTT D S. Sheaves and logic[M] //Applications of Sheaves. Berlin: Springer, 1979: 302-401.
[12] HÖHLE U. Quotients with respect to similarity relations[J]. Fuzzy Sets and Systems, 1988, 27(1):31-44.
[13] FILEP L. Study of fuzzy algebras and relations from a general viewpoint[J]. Computer Science, 1998, 14:49-55.
[14] DEMIRCI M. Foundations of fuzzy functions and vague algebra based on many-valued equivalence relations, part I: fuzzy functions and their applications[J]. International Journal of General Systems, 2003, 32(2):123-155.
[15] DEMIRCI M. L-equivalence relations on L-fuzzy sets, L-partitions of L-fuzzy sets and their one-to-one connections[J]. International Journal of Approximate Reasoning, 2019, 111:21-34.
[16] DI NOLA A, GERLA G. Lattice valued algebras [J]. Stochastica, 1987, 11(2/3):137-150.
[17] KURAOKA T, SUZUKI N Y. Lattice of fuzzy subalgebras in universal algebra[J]. Algebra Universalis, 2002, 47(3):223-237.
[18] FOKA S V, TONGA M. A note on the algebraicity of L-fuzzy subalgebras in universal algebra[J]. Soft Computing, 2020, 24(2):895-899.
[19] SESELJA B, TEPAVCEVIC A. Ω-algebras[C] //2015 IEEE Symposium Series on Computational Intelligence. Cape Town, South Africa: IEEE, 2015: 971-975.
[20] BUDIMIROVIC B, BUDIMIROVIC V, SESELJA B, et al. E-fuzzy groups[J]. Fuzzy Sets and Systems, 2016, 289:94-112.
[21] SESELJA B, TEPAVCEVIC A. L-E-fuzzy lattices[J]. International Journal of Fuzzy Systems, 2015, 17(3):366-374.
[22] KRAPEZ A,SESELJA B, TEPAVCEVIC A. Solving linear equations by fuzzy quasigroups techniques[J]. Information Sciences, 2019, 491:179-189.
[23] SESELJA B, TEPAVCEVIC A. Ω-groups in the language of Ω-groupoids[J]. Fuzzy Sets and Systems, 2020, 397:152-167.
[24] EDEGHAGBA E E. On ω-subgroup[J]. Gadau Journal of Pure and Allied Sciences, 2022, 1(1):55-67.
[25] JIMENEZ J, SERRANO M L, SESELJA B, et al. Omega-rings[J]. Fuzzy Sets and Systems, 2023, 455:183-197.
[1] 罗清君. Quantale的L-模糊理想[J]. 《山东大学学报(理学版)》, 2019, 54(12): 63-67.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!